Question: Simplify the following expression: $\dfrac{27n^3}{54n^5}$ You can assume $n \neq 0$.
Explanation: $ \dfrac{27n^3}{54n^5} = \dfrac{27}{54} \cdot \dfrac{n^3}{n^5} $ To simplify $\frac{27}{54}$ , find the greatest common factor (GCD) of $27$ and $54$ $27 = 3 \cdot 3 \cdot 3$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(27, 54) = 3 \cdot 3 \cdot 3 = 27 $ $ \dfrac{27}{54} \cdot \dfrac{n^3}{n^5} = \dfrac{27 \cdot 1}{27 \cdot 2} \cdot \dfrac{n^3}{n^5} $ $\phantom{ \dfrac{27}{54} \cdot \dfrac{3}{5}} = \dfrac{1}{2} \cdot \dfrac{n^3}{n^5} $ $ \dfrac{n^3}{n^5} = \dfrac{n \cdot n \cdot n}{n \cdot n \cdot n \cdot n \cdot n} = \dfrac{1}{n^2} $ $ \dfrac{1}{2} \cdot \dfrac{1}{n^2} = \dfrac{1}{2n^2} $